Two-layer formulation for long-runout turbidity currents: theory and bypass flow case

Turbidity currents, which are stratified, sediment-laden bottom flows in the ocean or lakes, can run out for hundreds or thousands of kilometres in submarine channels without losing their stratified structure. Here, we derive a layer-averaged, two-layer model for turbidity currents, specifically designed to capture long-runout. A number of previous models have captured runout of only tens of kilometres, beyond which thickening of the flows becomes excessive, and the models without a lateral overspill mechanism fail. In our framework, a lower layer containing nearly all the sediment is a faster, gravity-driven flow that propels an upper layer, where sediment concentration is nearly zero. The thickness of the lower layer is controlled by competition between interfacial water entrainment due to turbulent mixing and water detrainment due to sediment settling at the interface. The detrainment mechanism, first identified in experiments, is the key feature that prevents excessive thickening of the lower layer and allows long-runout. Under normal flow conditions, we obtain an exact solution to the two-layer formulation, revealing a constant velocity and a constant thickening rate in each of the two layers. Numerical simulations applied to gradually varied flows on both constant and exponentially declining bed slopes, with boundary conditions mimicking field observations, show that the predicted lower layer thickness after 200 km flow propagation compares with observed submarine channel depths, whereas previous models overestimate this thickness three- to fourfold. This formulation opens new avenues for modelling the fluid mechanics and morphodynamics of long-runout turbidity currents in the submarine setting.